Root closed function algebras on compacta of large dimension
| dc.creator | Brodskiy, N. | |
| dc.creator | Dydak, J. | |
| dc.creator | Karasev, A. | |
| dc.creator | Kawamura, K. | |
| dc.date | 2005-09-01 | |
| dc.date.accessioned | 2026-07-07T09:23:37Z | |
| dc.date.available | 2026-07-07T09:23:37Z | |
| dc.description | Let $X$ be a Hausdorff compact space and $C(X)$ be the algebra of all continuous complex-valued functions on $X$, endowed with the supremum norm. We say that $C(X)$ is (approximately) $n$-th root closed if any function from $C(X)$ is (approximately) equal to the $n$-th power of another function. We characterize the approximate $n$-th root closedness of $C(X)$ in terms of $n$-divisibility of first $\check {\rm C}$ech cohomology groups of closed subsets of $X$. Next, for each positive integer $m$ we construct $m$-dimensional metrizable compactum $X$ such that $C(X)$ is approximately $n$-th root closed for any $n$. Also, for each positive integer $m$ we construct $m$-dimensional compact Hausdorff space $X$ such that $C(X)$ is $n$-th root closed for any $n$. | |
| dc.description | 10 pages | |
| dc.identifier | https://arxiv.org/abs/math/0509006 | |
| dc.identifier | http://arxiv.org/abs/math/0509006 | |
| dc.identifier | Proc. Amer. Math. Soc. 135 (2007), 587--596. | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/155800 | |
| dc.subject | Functional Analysis | |
| dc.subject | General Topology | |
| dc.subject | 54F45; 46J10 | |
| dc.title | Root closed function algebras on compacta of large dimension | |
| dc.type | text |